Abstract
In this chapter we explain reduced density matrix and its applications in molecular modeling. While traditional methods for computing the orbitals are scaling cubically with respect to the number of electrons, the computation of the density matrix offers the opportunity to achieve linear complexity. We describe several iteration schemes for the computation of the density matrix. We briefly present the concept of best n-term approximation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Gidofalvi G, Mazziotti D (2004) Variational reduced-density-matrix theory: strength of Hamiltonian-dependent positivity conditions. Chem Phys Lett 398:4-6
Yang M (2005) A reduced density-matrix theory of absorption line shape of molecular aggregate. J Chem Phys 123:12 pp 124705–124706
Collins DM (1993) Entropy on charge density: making the quantum mechanical connection. Acta Cryst D49 pp 86-89
Fukuda M et al. (2007) Large-scale semidefinite programs in electronic structure calculation. Math Prog 109:2–3
McRae WB, Davidson ER (1972) Linear inequalities for density matrices II. J Math Phys 13:1527
Garrod C, Fusco MA (1976) Role of Model System in Few-Body Reduction of N-Fermion Problem. Int J Quant Chem 10:495
Vandenberghe L, Boyd S (1996) Semidefinite programming. SIAM 38: 49
Wolkowicz H, Saigal R, Vandenberghe L (2000) Handbook of Semidefinite Programming: Theory, Algorithms, and Applications. Kluwer Academic, Norwell, MA
Nakata M, Nakatsuji H, Ehara M, Fukuda M, Nakata K, Fujisawa K (2001) Variational calculations of fermion second-order reduced density matrices by a semidefinite programming algorithm. J Chem Phys 114:8282
Jacobs V et al. (2007) Advanced Optical and Quantum Memories and Computing IV. Proc SPIE 6482 pp 64820X
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
(2008). Reduced Density Matrix. In: Computational Chemistry and Molecular Modeling. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77304-7_10
Download citation
DOI: https://doi.org/10.1007/978-3-540-77304-7_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77302-3
Online ISBN: 978-3-540-77304-7
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)